Learning Nonlinear Dynamic Models from Non-sequenced Data
(2010)

Abstract

Virtually all methods of learning dynamic
systems from data start from the same basic
assumption: the learning algorithm will
be given a sequence of data generated from
the dynamic system. We consider the case
where the training data comes from the system’s
operation but with no temporal ordering.
The data are simply drawn as individual
disconnected points. While making this assumption
may seem absurd at first glance,
many scientific modeling tasks have exactly
this property.

Previous work proposed methods for learning
linear, discrete time models under these assumptions
by optimizing approximate likelihood
functions. We extend those methods to
nonlinear models using kernel methods. We
go on to propose a new approach that focuses
on achieving temporal smoothness in
the learned dynamics. The result is a convex
criterion that can be easily optimized and often
outperforms the earlier methods. We test
these methods on several synthetic data sets
including one generated from the Lorenz attractor.